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- Hitoshi Furusawa, Yasuo Kawahara, +9 authors Noriko Sugimoto
- 1998

The aim of this thesis is to develop the fuzzy relational calculus. To develop this calculus, we study four algebraic formalisations of fuzzy relations which are called fuzzy relation algebras, Zadeh categories, relation algebras and Dedekind categories, and we strive to arrive at their representation theorems. The calculus of relations has been… (More)

- Yasuo Kawahara, Hitoshi Furusawa
- Fuzzy Sets and Systems
- 1999

This paper provides an algebraic formalization of mathematical structures formed by fuzzy relations with sup-min composition. A simple proof of a representation theorem for Boolean relation algebras satisfying Tarski rule and point axiom has been given by G. Schmidt and T. Strohlein. Unlike Boolean relation algebras, fuzzy relation algebras are not Boolean… (More)

- Hitoshi Furusawa, Georg Struth
- ACM Trans. Comput. Log.
- 2015

We reconstruct Peleg’s concurrent dynamic logic in the context of modal Kleene algebras. We explore the algebraic structure of its multirelational semantics and develop an axiomatization of concurrent dynamic algebras from that basis. In this context, sequential composition is not associative. It interacts with parallel composition through a weak… (More)

- Toshinori Takai, Hitoshi Furusawa
- RelMiCS
- 2006

- Yasuo Kawahara, Hitoshi Furusawa, Masao Mori
- Inf. Sci.
- 1997

This paper provides a notion of Zadeh categories as a categorical structure formed by fuzzy relations with sup-min composition, and proves two representation theorems for Dedekind categories (relation categories) with a unit object analogous to one-point set, and for Zadeh categories without unit objects.

- Yasuo Kawahara, Hitoshi Furusawa
- RelMiCS
- 2000

This paper studies notions of scalar relations and crispness of relations.

- Hitoshi Furusawa, Norihiro Tsumagari, Koki Nishizawa
- RelMiCS
- 2008

- Hitoshi Furusawa, Georg Struth
- ACM Trans. Comput. Log.
- 2016

Binary multirelations generalise binary relations by associating elements of a set to its subsets. We study the structure and algebra of multirelations under the operations of union, intersection, sequential, and parallel composition, as well as finite and infinite iteration. Starting from a set-theoretic investigation, we propose axiom systems for… (More)

This paper provides a proof of a representation theorem for homogeneous relation algebras by using concepts of scalar relations and point relations.

- Koki Nishizawa, Norihiro Tsumagari, Hitoshi Furusawa
- RelMiCS
- 2009